Performance
The ellipsoid method is used on low-dimensional problems, such as planar location problems, where it is numerically stable. On even "small"-sized problems, it suffers from numerical instability and poor performance in practice.
However, the ellipsoid method is an important theoretical technique in combinatorial optimization. In computational complexity theory, the ellipsoid algorithm is attractive because its complexity depends on the number of columns and the digital size of the coefficients, but not on the number of rows. In the 21st century, interior-point algorithms with similar properties have appeared.
Read more about this topic: Ellipsoid Method
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